Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

TL;DR

This study investigates the violation of the fluctuation-dissipation theorem in spin ice models, revealing variable-dependent effective temperatures during non-equilibrium dynamics and providing insights into monopole behavior and glassy states.

Contribution

It demonstrates the existence of variable-dependent effective temperatures in spin ice during non-equilibrium conditions, extending understanding of FDT violations in frustrated magnetic systems.

Findings

FDT holds at low temperatures in local equilibrium.

Non-equilibrium dynamics show FDT violations after thermal quench.

Different variables exhibit distinct effective temperatures.

Abstract

We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4$ K below which the system completely freezes. Non-equilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the non-contractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective non-equilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir, the monopole concentration responds with a lower effective temperature while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.